Our next physics colloquium will take place on February 2 at 12 noon sharp. Prof. Dr. Jasper van Wezel is Professor of Condensed Matter Theory at the University of Amsterdam. The topic of his lecture is "(Non-)invertible symmetry and spontaneous duality breaking."
Symmetries are one of the cornerstones of our modern understanding of physics. The mathematical notion of symmetry, however, has been steadily generalized over the past few years, to include for example higher-form, latent, asymptotic, and even non-invertible symmetries. Within condensed matter physics, non-invertible symmetry has been suggested to arise in connection with duality, which is a second organizational cornerstone used throughout all realms of modern physics. The fruit fly model used to describe and understand this type of non-invertible symmetry and its connection to duality is the well-known (transverse field) Ising model, whose universal, emergent properties have been used to model phenomena ranging from classical statistical physics, via quantum materials and particle physics, to cosmological scales.
The Ising model was famously "solved" by Kramers and Wannier, using its self-duality. This duality is not exact, and the original and dual models have different symmetries and numbers of ground states. As a consequence, the duality is traditionally described in terms of a so-called non-invertible symmetry.
In this colloquium, I will review this construction and argue that requiring an exact bulk duality gives rise to the emergence of an anomalous degree of freedom at the boundaries of the Ising magnet, akin to the celebrated bulk-boundary correspondence in topological phases of matter.
This in turn leads to a paradox: the spontaneous breaking of a global symmetry in the bulk Ising model can equivalently be described as spontaneously breaking a local, boundary-based, symmetry in the dual system. This seemingly contradicts Elitzur’s theorem. I will show that the paradox can be resolved by introducing the concept of spontaneous duality breaking. While the original and dual models are mathematically equivalent, only one is sensitive to spatially local perturbations in any actual implementation, thereby breaking the duality.
Abstract of Prof. van Wezel's lecture
Prof. Dr. Ilya Eremin gives an introduction to the lecture.
The faculty cordially invites all interested parties. The event will take place in lecture hall HZO 20.